Problem
9. Multiply the polynomials. \[ \left(4 b^{2} z^{2}+4 b z\right)\left(-2 b^{3} z-2 z^{3}+6 z^{2}+5 z\right) \]
Solution
Step 1 ：\( (4 b^{2} z^{2} + 4 b z) (-2 b^{3} z - 2 z^{3} + 6 z^{2} + 5 z) \)
Step 2 ：\( 4 b^{2} z^{2}(-2 b^{3} z - 2 z^{3} + 6 z^{2} + 5 z) + 4 b z(-2 b^{3} z - 2 z^{3} + 6 z^{2} + 5 z) \)
Step 3 ：\( -8 b^{5} z^{3} -8 b^{2} z^{5} + 24 b^{2} z^{4} + 20 b^{2} z^{3} -8 b^{4} z^{2} - 8 b z^{4} + 24 b z^{3} + 20 b z^{2} \)
